New proofs for three identities of seventh order mock theta functions

Lijun Hao; Lijun Hao

doi:10.3934/math.2023238

AIMS Mathematics

2023, Volume 8, Issue 2: 4806-4813. doi: 10.3934/math.2023238

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New proofs for three identities of seventh order mock theta functions

Lijun Hao ^,

School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China

Received: 19 October 2022 Revised: 29 November 2022 Accepted: 02 December 2022 Published: 08 December 2022
MSC : 11F27, 33D15

Using the three-term Weierstrass relation for theta functions and the properties of Hecke-type double sums and Appell-Lerch sums, we give new and simple proofs for the seventh order mock theta conjectures.
- mock theta functions,
- Hecke-type double sums,
- Appell-Lerch sums,
- the three-term Weierstrass relation
Citation: Lijun Hao. New proofs for three identities of seventh order mock theta functions[J]. AIMS Mathematics, 2023, 8(2): 4806-4813. doi: 10.3934/math.2023238

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Abstract

Using the three-term Weierstrass relation for theta functions and the properties of Hecke-type double sums and Appell-Lerch sums, we give new and simple proofs for the seventh order mock theta conjectures.

References

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